The Projection software package aids the design and optimization of electron and ion beam projection systems for high-throughput lithography, where an electron or ion beam passes through a rectangular region of a mask.  The formed rectangular shaped beam may be centered either on or off the optical axis.  A system of magnetic or electrostatic projection lenses is then used to form a demagnified image of this rectangular shaped beam at a target plane. The lenses can be magnetic, electrostatic or both.  An aperture is generally placed between the two sets of lenses.  Two groups of deflectors, which can be either magnetic or electrostatic, can also be located on each side of the aperture.  If the shaped beam is centered off-axis, the deflectors can steer the beam though the lenses along a modified path to reduce the aberrations, and thereby act mainly as aberration-reduction elements, rather than as conventional deflectors.  A conventional projection system, in which the projected area of the mask is centered on the optical axis, is simply a special case of the system shown above, with the shaped beam centered on the axis, and the deflectors either switched off or omitted. 

PROJECTION computes the optical properties of such systems, including the geometrical aberrations of 3rd-order and 5th-order and chromatic aberrations of up to 4th rank.  The software can also refine the design to optimize the optical performance.  The properties of dynamic correction elements (i.e. stigmators and dynamic focus lenses) can be computed.  Several graphical post-processing facilities are included in PROJECTION for plotting the principal paraxial rays, the lens and deflector axial field functions, aberration spot diagrams in the image plane and current density contours in the final spot.